It should work on the DX160. As for stuttering, it might be the implementation of the apple codecs that cause this, or might have just been the app the OP was playing them through, or loaded down OS (multiple apps running), etc... It is unknown at this point, and I don't have anything of that bitrate to test (I am not in the Apple ecosystem). Although, I have read about the app itself having stuttering/freezing/skipping bugs when it was released back in Jul of 2021.
I have some music that is .alac that is 16/44 but I over sample it in Neutron to 352 ( x 8 multiplier, which is max on this player) with no stutters. Though, I cannot do PCM to DSD256 (or 128) on the DX160, though I can on the DX300. I do not use Apple Lossless (app) for anything though. I know this may seem irrelevant, but doing this taxes the CPU, and I was trying to see if doing this might cause some stuttering (doing conversions on the fly). Not a true test, but best I can do with my current selection of .alac music, I'm afraid. Hate to say it, but you may have to just pull the trigger and experiment. Unless you will ONLY listen to Apple Lossless, you can always switch to .flac or something similar (they all work flawlessly).
Sorry I couldn't be more help!